Final answer:
The statement is false that either Tiger Woods and Maria Sharapova play professional football or Drew Brees and Serena Williams play professional baseball.
Step-by-step explanation:
To represent the statement in the question, let's define the following:
T = Tiger Woods plays professional football.
M = Maria Sharapova plays professional football.
D = Drew Brees plays professional baseball.
S = Serena Williams plays professional baseball.
The given statement is:
It is not the case that either (T and M) or (D and S) is true.
This can be written as: ¬[(T ∧ M) ∨ (D ∧ S)].
We can simplify the statement using De Morgan's Laws and Logical Equivalences:
¬[(T ∧ M) ∨ (D ∧ S)] = (¬T ∨ ¬M) ∧ (¬D ∨ ¬S).
So, the simplified statement is: (¬T ∨ ¬M) ∧ (¬D ∨ ¬S).
This means that it is false that either Tiger Woods and Maria Sharapova play professional football or Drew Brees and Serena Williams play professional baseball. Both parts of the statement must be false for the statement to be true.